The dual minimum distance of arbitrary-dimensional algebraic-geometric codes

Alain Couvreur

doi:10.1016/j.jalgebra.2011.09.030

The dual minimum distance of arbitrary-dimensional algebraic-geometric codes

Alain Couvreur

INRIA

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, the minimum distance of the dual C^⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field F_q is studied. The approach is based on problems à la Cayley-Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some degree m. If X is a curve, the result improves in some situations the well-known Goppa designed distance.

Original language	English
Pages (from-to)	84-107
Number of pages	24
Journal	Journal of Algebra
Volume	350
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.09.030
Publication status	Published - 15 Jan 2012
Externally published	Yes

Keywords

Algebraic geometry
Algebraic-geometric codes
Error-correcting codes
Finite fields
Linear systems

Access to Document

10.1016/j.jalgebra.2011.09.030

Cite this

@article{6cdf90e123b840d3b2fe2ef4f330ae34,

title = "The dual minimum distance of arbitrary-dimensional algebraic-geometric codes",

abstract = "In this article, the minimum distance of the dual C⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field Fq is studied. The approach is based on problems {\`a} la Cayley-Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some degree m. If X is a curve, the result improves in some situations the well-known Goppa designed distance.",

keywords = "Algebraic geometry, Algebraic-geometric codes, Error-correcting codes, Finite fields, Linear systems",

author = "Alain Couvreur",

year = "2012",

month = jan,

day = "15",

doi = "10.1016/j.jalgebra.2011.09.030",

language = "English",

volume = "350",

pages = "84--107",

journal = "Journal of Algebra",

issn = "0021-8693",

number = "1",

}

TY - JOUR

T1 - The dual minimum distance of arbitrary-dimensional algebraic-geometric codes

AU - Couvreur, Alain

PY - 2012/1/15

Y1 - 2012/1/15

N2 - In this article, the minimum distance of the dual C⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field Fq is studied. The approach is based on problems à la Cayley-Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some degree m. If X is a curve, the result improves in some situations the well-known Goppa designed distance.

AB - In this article, the minimum distance of the dual C⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field Fq is studied. The approach is based on problems à la Cayley-Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some degree m. If X is a curve, the result improves in some situations the well-known Goppa designed distance.

KW - Algebraic geometry

KW - Algebraic-geometric codes

KW - Error-correcting codes

KW - Finite fields

KW - Linear systems

UR - https://www.scopus.com/pages/publications/82255175315

U2 - 10.1016/j.jalgebra.2011.09.030

DO - 10.1016/j.jalgebra.2011.09.030

M3 - Article

AN - SCOPUS:82255175315

SN - 0021-8693

VL - 350

SP - 84

EP - 107

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

The dual minimum distance of arbitrary-dimensional algebraic-geometric codes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this